Where Atmospheric Neutrinos Give Way: The Crossover Energy Against Two Astrophysical Spectra

Every astrophysical neutrino measurement is a subtraction: the atmospheric background, made in cosmic-ray air showers above the detector, falls steeply with energy while the astrophysical signal falls less steeply, and the energy where they cross defines the working range of the science. This paper computes that crossover against two published astrophysical spectra. With a schematic conventional atmospheric flux normalised to an E-squared level of 3.000e-06 at 10 TeV and falling with index 3.7, the crossover against the soft contained-event spectrum lies at 347 TeV, and against the harder through-going spectrum at 401 TeV. The prompt atmospheric component from charmed-meson decay, harder than the conventional flux, grows from 5.01 per cent of the conventional level at 100 TeV to 50.1 per cent at 1 PeV in this parameterisation — the background that will matter most for the next generation of measurements. The study is computed from stated assumptions, not measured.